Question

1. which shape naturally tessellates?

a. circle
b. pentagon
c. square
d. nonagon

Explanation:

• A circle cannot tessellate because there are gaps between them when trying to cover a plane.
• A regular pentagon has interior angles of \(108^{\circ}\), and \(360\div108\) is not an integer, so it cannot tessellate the plane without gaps or overlaps.
• A square has interior angles of \(90^{\circ}\), and \(360\div90 = 4\). So, squares can be arranged to cover a plane without gaps or overlaps.
• A nonagon (9 - sided polygon) has interior angles of \(\frac{(9 - 2)\times180^{\circ}}{9}=140^{\circ}\), and \(360\div140\) is not an integer, so it cannot tessellate the plane.

Answer:

C. Square